Triple

T19532117
Position Surface form Disambiguated ID Type / Status
Subject Hamming bound E488680 entity
Predicate comparedWith P278 FINISHED
Object Gilbert–Varshamov bound
The Gilbert–Varshamov bound is a fundamental result in coding theory that provides a lower bound on the maximum size of error-correcting codes for given length and minimum distance, showing that relatively dense codes with good error-correcting capability exist.
E1381501 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Gilbert–Varshamov bound | Statement: [Hamming bound, comparedWith, Gilbert–Varshamov bound]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gilbert–Varshamov bound
Context triple: [Hamming bound, comparedWith, Gilbert–Varshamov bound]
  • A. Hamming bound
    The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
  • B. Accola–Maclachlan bound
    The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
  • C. Golay code
    The Golay code is a highly symmetric, perfect error-correcting code in coding theory, notable for its deep connections to sporadic simple groups, sphere packings, and the Leech lattice.
  • D. Wozencraft ensemble in coding theory
    The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
  • E. Slepian–Wolf coding theorem
    The Slepian–Wolf coding theorem is a fundamental result in information theory that characterizes the limits of lossless data compression for correlated sources encoded separately but decoded jointly.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Gilbert–Varshamov bound
Triple: [Hamming bound, comparedWith, Gilbert–Varshamov bound]
Generated description
The Gilbert–Varshamov bound is a fundamental result in coding theory that provides a lower bound on the maximum size of error-correcting codes for given length and minimum distance, showing that relatively dense codes with good error-correcting capability exist.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gilbert–Varshamov bound
Target entity description: The Gilbert–Varshamov bound is a fundamental result in coding theory that provides a lower bound on the maximum size of error-correcting codes for given length and minimum distance, showing that relatively dense codes with good error-correcting capability exist.
  • A. Hamming bound
    The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
  • B. Accola–Maclachlan bound
    The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
  • C. Golay code
    The Golay code is a highly symmetric, perfect error-correcting code in coding theory, notable for its deep connections to sporadic simple groups, sphere packings, and the Leech lattice.
  • D. Wozencraft ensemble in coding theory
    The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
  • E. Slepian–Wolf coding theorem
    The Slepian–Wolf coding theorem is a fundamental result in information theory that characterizes the limits of lossless data compression for correlated sources encoded separately but decoded jointly.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8e8db5b6c8190984b61f91981f575 completed April 10, 2026, 12:11 p.m.
NER Named-entity recognition batch_69e6363fd1f8819080805346efad2579 completed April 20, 2026, 2:20 p.m.
NED1 Entity disambiguation (via context triple) batch_6a074e7b52d88190b0e095ce39d7a003 completed May 15, 2026, 4:48 p.m.
NEDg Description generation batch_6a074f6d79b88190a0b8442af2be0ed1 completed May 15, 2026, 4:53 p.m.
NED2 Entity disambiguation (via description) batch_6a074fed47bc8190b1a78dcc50345ca4 completed May 15, 2026, 4:55 p.m.
Created at: April 10, 2026, 1:41 p.m.